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Class 10MathematicsReal NumbersDecimal expansion of rational numbersHardLevel 20
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If (\frac{m}{735}) has a terminating decimal expansion, what factor must (m) contain at minimum?

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Answer and explanation

Correct answer: (147)

Step 1: (735=3\cdot 5\cdot 7^2). Step 2: For a terminating decimal, (3) and (7^2) must not remain in the reduced denominator. So (m) must contain (3\cdot 7^2=147). Step 3: The factor (5) may remain, but (3) and (7) must cancel.

Related tags

Minimum-FactorTerminating-ConditionPrime-FactorisationHard

Frequently asked questions

What is the correct answer to this question?

(147)

Why is this the correct answer?

Step 1: (735=3\cdot 5\cdot 7^2). Step 2: For a terminating decimal, (3) and (7^2) must not remain in the reduced denominator. So (m) must contain (3\cdot 7^2=147). Step 3: The factor (5) may remain, but (3) and (7) must cancel.

Which subject and chapter does this question cover?

This is a Class 10 Mathematics question. Chapter: Real Numbers. Topic: Decimal expansion of rational numbers.

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  1. 1What type of decimal expansion will the rational number (\frac{3}{8}) have?
  2. 2What type of decimal expansion does (\frac{5}{6}) have?
  3. 3Under what condition does (\frac{p}{q}) have a terminating decimal expansion when the fraction is in lowest form?
  4. 4After reducing (\frac{15}{40}), what type of decimal expansion will it have?
  5. 5After at most how many decimal places will the decimal expansion of (\frac{7}{16}) terminate?
  6. 6Choose the correct statement about the decimal expansion of (\frac{11}{45}).
  7. 7Which of the following fractions will give a terminating decimal?
  8. 8Which of the following fractions will give a non-terminating recurring decimal?
  9. 9When (0.75) is written as a rational number, which form is obtained?
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